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One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.
Number, Scientific American, 211, (Sept. 1964), 51 - 59.
Eratosthenes and the Mystery of the Stades
Most of what is known about Eratosthenes’ geometric argument comes from the writings of Cleomedes, in the first century BCE. Eratosthenes’ argument, as described by Cleomedes, gives the circumference of the Earth as approximately 250,000 stades. However, most other ancient authors give 252,000 stades as Eratosthenes’ value for the circumference of the Earth. Strabo’s Geography, written in the late first century BCE, cites Hipparchus as the source of this figure. Another reference to this length appears in a letter written by Heron of Alexandria (ca. 75 CE) in the second century CE [4, pp.60-63 ].
In light of the many textual references stating 252,000 stades as the circumference given by Eratosthenes, many scholars believe that the addition of 2000 stades was a correction made by Eratosthenes shortly after his original calculation.
What could be the reason for Eratosthenes’ correction? There are many theories as to why this correction may have been made. Let use examine three prevailing theories.
Having established that Eratosthenes probably gave 252,000 stades as his best approximation of the Earth’s circumference, and given four stade lengths which might represent reasonable approximations of the stade used by Eratosthenes, it is now possible to obtain some modern equivalents to Eratosthenes’ approximation. Below is a table listing four approximations of the Earth’s circumference by Eratosthenes’ method, using each of the four previously mentioned types of stade.